Albinism, an autosomal recessive trait characterized by an absence of skin pigmentation, is found in 1 in 4000 people in populations at equilibrium. Brachydactyly, an autosomal dominant trait producing shortened fingers and toes, is found in 1 in 6000 people in populations at equilibrium. For each of these traits, calculate the frequency of heterozygotes in the population

Verified step by step guidance

1. Step 1: Understand the problem. Albinism is an autosomal recessive trait, meaning individuals with the condition have two copies of the recessive allele (aa). Brachydactyly is an autosomal dominant trait, meaning individuals with the condition have at least one dominant allele (Bb or BB). We are tasked with calculating the frequency of heterozygotes (Aa for albinism and Bb for brachydactyly) in the population.
2. Step 2: Use the Hardy-Weinberg equilibrium principle. For a population at equilibrium, the allele frequencies can be used to calculate genotype frequencies. The Hardy-Weinberg equation is p² + 2pq + q² = 1, where p is the frequency of the dominant allele, q is the frequency of the recessive allele, p² is the frequency of homozygous dominant individuals, 2pq is the frequency of heterozygotes, and q² is the frequency of homozygous recessive individuals.
3. Step 3: Calculate the allele frequencies for albinism. Since the frequency of individuals with albinism (aa) is given as 1 in 4000, this corresponds to q² = 1/4000. Solve for q, the frequency of the recessive allele, by taking the square root of q². Then, calculate p, the frequency of the dominant allele, using the relationship p + q = 1.
4. Step 4: Calculate the frequency of heterozygotes for albinism. Using the Hardy-Weinberg equation, the frequency of heterozygotes (Aa) is given by 2pq. Multiply the calculated values of p and q by 2 to find the heterozygote frequency for albinism.
5. Step 5: Repeat the process for brachydactyly. Since the frequency of individuals with brachydactyly (BB or Bb) is given as 1 in 6000, this corresponds to p² + 2pq = 1/6000. Use the Hardy-Weinberg equation to estimate p and q, and then calculate the frequency of heterozygotes (Bb) using 2pq.

Key Concepts

Hardy-Weinberg Principle

The Hardy-Weinberg Principle provides a mathematical framework for understanding genetic variation in a population at equilibrium. It states that allele and genotype frequencies will remain constant from generation to generation in the absence of evolutionary influences. This principle allows for the calculation of allele frequencies and the expected proportions of genotypes, including heterozygotes, based on observed trait frequencies.

Autosomal Recessive Inheritance

Autosomal recessive inheritance refers to a pattern where two copies of a mutated gene are necessary for an individual to express a trait, such as albinism. In this case, individuals with one normal and one mutated allele (heterozygotes) do not exhibit the trait but can pass the mutated allele to their offspring. Understanding this inheritance pattern is crucial for calculating the frequency of heterozygotes in a population.

Autosomal Dominant Inheritance

Autosomal dominant inheritance occurs when only one copy of a mutated gene is sufficient to express a trait, such as brachydactyly. Individuals with the dominant allele will show the trait, while those with two normal alleles will not. This concept is essential for determining the frequency of heterozygotes, as it influences the expected genotype ratios in the population based on the trait's prevalence.